For whatever it's worth, the novels have established that Federation-Cardassian first contact took place in 2327, during the administration of Federation President Thelianaresth "Thelian" th'Vorothishria of Andor.
Building on this for anyone who's interested in the novels:
As
Sci said, we've had 2327 given as official first contact in several novels, including
The Art of the Impossible (building on "Enter the Wolves", a comic book, that established the date;
The Art of the Impossible directly references a conference at Legara from EtW, as does its fellow "Lost Era" novel
Well of Souls). Then there was 2321 given by a Maquis in
The Brave and the Bold as the
real first contact between Federation and Cardassian interests - civilian exchange on outer colonies, before the governments or militaries got involved. Finally, the novel
Day of the Vipers hints at ship-based contact, fly-bys and skirmishes, for over a decade before that. So again, we've got varying degrees of contact, with 2327 accepted as the first "true" meeting between people in service to the UFP and Cardassian governments. But even then the novels seem to accept that prior to actual contact there would be knowledge and exchange in an unofficial capacity.
From all this, and being a novel fan who likes to incorporate their ideas if possible, I assume that ships identified as Cardassian begin getting involved in fights with Federation-affiliated vessels along the border region around about the 2310s. Eventually, official first contact is made in 2327, after a few decades of unofficial "buzzings" and border incidents (and snooping around Bajor, according to
Day of the Vipers). And then Central Command blows any chance of good relations with its treachery at Legara (see
Enter the Wolves), which in turn leads the Detapa Council and Obsidian Order to try and mend the relationship by having the UFP mediate the Betreka conflict the following year (
The Art of the Impossible).
